We compute thermal transport coefficients for glassy and liquid water in terms of the normal modes of the glass. We find the thermal diffusivity at 300 K to be close to the actual value of 15 Angstrom(2) ps(-1), indicating that this property arises largely from the vibrations of the water network. The computed thermal conductivity is about a factor of 2 smaller than the actual value of 6.1 mW cm(-1) K-1 for liquid water at 300 K, due to neglect of the configurational contribution to the heat capacity. (C) 2004 Published by Elsevier B.V.